Diophantine Analysis, written by Robert Daniel Carmichael and first published in 1915, is a mathematical treatise that focuses on the study of Diophantine equations. Diophantine equations are polynomial equations with integer coefficients, and the book explores various methods for solving them. The book is divided into two parts. The first part covers the basics of Diophantine equations, including linear equations, quadratic equations, and Pell's equation. The second part delves deeper into more complex equations, such as cubic equations, quartic equations, and equations with more than two variables. Throughout the book, Carmichael provides numerous examples and exercises to help readers understand the concepts presented. He also includes historical background and references to the work of other mathematicians who have contributed to the field of Diophantine analysis. Diophantine Analysis is considered a classic in the field of number theory and has been widely used as a textbook for advanced mathematics courses. It is a valuable resource for students and researchers interested in the study of Diophantine equations and their applications in various fields, including cryptography and computer science.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.